A solid catalyst component for .alpha.-olefin polymerization, which comprises a titanium atom, a magnesium atom, a halogen atom, a phthalic acid ester compound, and a 1,3-diether compound, wherein an amount of the 1,3-diether compound contained in the solid catalyst component is 0.1 to 3 mol per one mol of the phthalic acid ester compound contained therein; a process for producing a catalyst for .alpha.-olefin polymerization, which comprises the step of contacting at least the above solid catalyst component, an organoaluminum compound, and an external electron donor compound with one another; and a process for producing an .alpha.-olefin polymer, which comprises the step of homopolymerizing or copolymerizing an .alpha.-olefin in the presence of a catalyst produced by the above process.